Sets of Finite Perimeter and Geometric Variational Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sets of Finite Perimeter and Geometric Variational Problems write by Francesco Maggi. This book was released on 2012-08-09. Sets of Finite Perimeter and Geometric Variational Problems available in PDF, EPUB and Kindle. The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.
Sets of Finite Perimeter and Geometric Variational Problems
Sets of Finite Perimeter and Geometric Variational Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sets of Finite Perimeter and Geometric Variational Problems write by Francesco Maggi. This book was released on 2012-08-09. Sets of Finite Perimeter and Geometric Variational Problems available in PDF, EPUB and Kindle. An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
Sets of Finite Perimeter and Geometric Variational Problems
Sets of Finite Perimeter and Geometric Variational Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sets of Finite Perimeter and Geometric Variational Problems write by Francesco Maggi. This book was released on 2014-05-14. Sets of Finite Perimeter and Geometric Variational Problems available in PDF, EPUB and Kindle. An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
Minimal Surfaces and Functions of Bounded Variation
Minimal Surfaces and Functions of Bounded Variation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Minimal Surfaces and Functions of Bounded Variation write by Giusti. This book was released on 2013-03-14. Minimal Surfaces and Functions of Bounded Variation available in PDF, EPUB and Kindle. The problem of finding minimal surfaces, i. e. of finding the surface of least area among those bounded by a given curve, was one of the first considered after the foundation of the calculus of variations, and is one which received a satis factory solution only in recent years. Called the problem of Plateau, after the blind physicist who did beautiful experiments with soap films and bubbles, it has resisted the efforts of many mathematicians for more than a century. It was only in the thirties that a solution was given to the problem of Plateau in 3-dimensional Euclidean space, with the papers of Douglas [DJ] and Rado [R T1, 2]. The methods of Douglas and Rado were developed and extended in 3-dimensions by several authors, but none of the results was shown to hold even for minimal hypersurfaces in higher dimension, let alone surfaces of higher dimension and codimension. It was not until thirty years later that the problem of Plateau was successfully attacked in its full generality, by several authors using measure-theoretic methods; in particular see De Giorgi [DG1, 2, 4, 5], Reifenberg [RE], Federer and Fleming [FF] and Almgren [AF1, 2]. Federer and Fleming defined a k-dimensional surface in IR" as a k-current, i. e. a continuous linear functional on k-forms. Their method is treated in full detail in the splendid book of Federer [FH 1].
Geometric Flows on Planar Lattices
Geometric Flows on Planar Lattices - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Flows on Planar Lattices write by Andrea Braides. This book was released on 2021-03-23. Geometric Flows on Planar Lattices available in PDF, EPUB and Kindle. This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
